Wireless communication systems may transfer data between a transmitter and one or more receivers. The operation of wireless communication systems may be governed, for example, by standards such as the IEEE 802.11 family of standards. Receivers in a wireless communication system typically use one or more analog-to-digital converters (ADCs) to convert a received analog signal to a digital signal that may be processed to recover the transmitted data.
Techniques for sampling a received analog signal typically fall into one of two categories: uniform sampling and non-uniform sampling. In uniform sampling approaches, the received signal is sampled at uniform time intervals using a sampling clock. For example, FIG. 1A illustrates a uniform sampler and quantizer (Q), where a time-continuous analog input signal x(t) is first low-pass filtered, and then sampled with a clock signal having a sampling period t=nT and then quantized to produce a digital output signal x[n]. Although uniform sampling techniques provide predictability in terms of sampling intervals, the Nyquist theorem calls for the sampling clock to be at least twice the highest frequency component present in the sampled signal to prevent aliasing. In practice, the analog signal first passes through an anti-alias low-pass filter to attenuate high frequency content above the half of the sampling frequency to prevent aliasing. There is hence a tradeoff between the complexity of the anti-alias low-pass filter and the sampling clock frequency. Most modern communications systems employ a sampling clock that is several times greater than the Nyquist rate to ease the anti-alias filtering requirements. Thus, one disadvantage of the uniform sampling approach is the cost and complexity of implementing an analog anti-alias filter and a high-speed sampling clock in the receiver unit.
In non-uniform sampling approaches, the received signal can be sampled in response to the signal crossing one of the discrete quantized levels, thereby minimizing sampling or quantization errors. As long as the sampler can respond fast enough to the input signal, no aliasing effect is introduced by the non-uniform sampling. However, because the quantized samples of the input signal are taken at variable intervals depending on the signal, it is necessary to keep track of precisely when each sample of the input signal is quantized to correctly reconstruct the input signal from the quantized data. For example, FIG. 1B illustrates non-uniform sampling in which the input signal x(t) is sampled and quantized in non-equidistant intervals (nT+Δt[n]), resulting in an output signal x[n]+e[n] having an ideal equidistant sampled signal x[n] and an amplitude error e[n], where e[n] represents the difference in amplitude between the uniformly sampled signal and the realistic non-uniformly sampled signal, and where Δt represents the time offset from the ideal equidistant sample period nT. FIG. 1C illustrates reconstruction of the input signal using digital techniques in which a reconstructed signal xr[n] is created from the non-uniformly sampled signal x[n]+e[n] and the known time offset Δt[n]. Reconstructing non-uniformly sampled input signals is done in the digital domain. That is, with non-uniform sampling, the analog anti-alias filter is replaced by a digital circuit that is more robust and amenable to technology scaling.
Thus, there is a need for a simpler and more area-efficient circuit that can sample input signals in a non-uniform manner, thereby alleviating the need for high-speed sampling clocks while minimizing the undesirable effects of aliasing.
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